Achieving an 895 km Orbit: Calculating v

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In summary, the conversation is about calculating the velocity needed for a satellite to reach an orbit with an altitude of 895 km. The formula -μ*m/r is used, with μ being the standard gravitational parameter for Earth and R representing the distance from Earth's surface. The conversation also mentions adding this calculated velocity to 7404.5 m/s.
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How fast must a satellite leave Earth's surface to reach an orbit with an altitude of 895 km?

Ek + Eg (earth) = 1/2 Eg

(could you please show how to substitute to solve for v)

this question is on the forum and it was suggested to add this v once calculated to 7404.5 m/s which was calculated from v= square root of GM/r.
 
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Welcome to PF.

PE + KE = PE + KE

What they want to know is the KE at launch to end in the PE and KE in orbit.
 
  • #3


could you please show how to substitute for this equation? for 1/2mv squared i do not know what to use for mass.
 
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  • #4


Your PE at any point is given by -GMm/r. We will shorten that to -μ*m/r

μ = GMe is the standard gravitational parameter for Earth = 398,000 km³/s²
http://en.wikipedia.org/wiki/Standard_gravitational_parameter

This means that

-μm/Rearth + 1/2*m*V2launch = -μm/Rorbit + 1/2*m*Vorbit2

The mass of the object drops out.

V2launch = 2*(μ/Rearth -μ/Rorbit) + Vorbit2
 
  • #5


Thank-you so much!
 

FAQ: Achieving an 895 km Orbit: Calculating v

What is an 895 km orbit?

An 895 km orbit is a specific type of orbit around a celestial body, in which an object or spacecraft is positioned at a distance of 895 kilometers from the surface of the body. This distance is important for various reasons, including communication, observation, and exploration purposes.

Why is calculating v important for achieving an 895 km orbit?

Calculating v, or velocity, is important for achieving an 895 km orbit because it determines the speed at which an object or spacecraft must travel in order to maintain a stable orbit at the desired distance from the celestial body. Without the correct velocity, the object may either crash into the body or drift away from it.

How is v calculated for achieving an 895 km orbit?

V is calculated using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the celestial body, and r is the distance between the object and the body. This formula takes into account the gravitational pull of the body and the centrifugal force of the orbiting object, and helps determine the required velocity for maintaining the orbit.

What factors can affect the calculated v for an 895 km orbit?

The calculated v for an 895 km orbit can be affected by a number of factors, including the mass of the celestial body, the altitude of the orbit, and any external forces acting on the object or spacecraft. These factors may change the required velocity and must be taken into consideration during the calculation process.

How accurate do the calculations for achieving an 895 km orbit need to be?

The calculations for achieving an 895 km orbit need to be as accurate as possible in order to ensure a successful mission. Even small errors in the calculation of v can lead to significant differences in the object's orbit, potentially resulting in a failed mission. Therefore, it is important for scientists to use precise and advanced calculation methods for achieving an 895 km orbit.

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